In recent years, considerable effort has been devoted to developing small, economical and reliable angular rate sensors for use in inertial navigation systems and other applications. Although these efforts have resulted in the development of new gyroscopic devices such as the ring laser gyro and the dry-tuned-rotor two axes gyroscope, gyroscopic devices still present fairly significant size, cost and reliability tradeoffs. This is especially true relative to inertial navigation systems which require the precise measurement of the three components of specific force along the axes of the vessel or object being navigated and the three components of angular rate about those axes. The problem becomes even more significant in strapdown inertial navigation systems because such systems require a large dynamic range of angular rate measurement and long-term, null-point stability.
Accordingly, effort also has been directed to developing angular rate sensors that operate on principles other than gyroscopic effect. In one such proposal, one or more accelerometers are mounted with the force sensing axis of each accelerometer being parallel to and spaced apart from a Cartesian coordinate axis of the body whose rotation is to be measured and with each accelerometer being cyclically displaced (oscillated) along a predetermined path. In these arrangements, the output signal provided by each accelerometer includes specific force and Coriolis components that can be processed to provide a signal representative of specific force along a first coordinate axis of the coordinate system and, in addition, signal components that are representative of the angular rate about the second and third axes of the coordinate system. Thus, such arrangements can utilize as few as three accelerometers to provide measurement of the three specific force components and three angular rate components that fully describe the motion of a body that is moving in space (e.g., an aircraft, space vehicle or other object that is being navigated).
Merhav U.S. Pat. No. 4,445,376, issued on May 1, 1984, discloses an arrangement of the above-described type in which three accelerometers supply output signals that can be processed to provide the specific force components and the angular rate components relative to each axis of a righthand Cartesian coordinate system that is fixed within a moving body. In the arrangement disclosed in U.S. Pat. No. 4,445,376, each accelerometer is mounted so that the force sensitive axis of the accelerometer is parallel to an axis of the coordinate system (e.g., the X axis). In addition each accelerometer is mounted (or internally configured) so that the force sensitive axis rotates at a uniform rate about a fixed axis which is parallel to and spaced apart from the force sensitive axis. As the object with which the coordinate system is associated moves in space, the signal that is generated by each accelerometer includes a component representative of specific force along the coordinate direction in which the accelerometer force sensitive axis points and signal components representative of angular rate relative to the coordinate axes that are perpendicular to the accelerometer force sensitive axis. For example, in the specific arrangement disclosed in U.S. Pat. No. 4,445,376, the accelerometer that generates a signal representative of the X axis component of specific force and the Y and Z axes components of angular rate has the force sensitive axis of the accelerometer parallel to the X axis and rotates about a fixed axis of the coordinate system so that the force sensitive axis remains parallel to the X axis and circles the fixed axis at a constant radius.
In the signal processing arrangement disclosed in U.S. Pat. No. 4,445,376, each angular rate signal is obtained from an accelerometer output signal by a synchronous detection process in which the accelerometer output signal is modulated by a periodic function that is synchronized to the rotation of the accelerometer (e.g., the algebraic sign of cos .omega.t, where .omega. represents the rate at which the accelerometer moves about its center of rotation). The modulated signal is then integrated over the period required for the accelerometer to complete one revolution and the resulting signal is scaled to provide the angular rate signal. The specific force signal is obtained by integrating the accelerometer output over a rotational period (without modulation of the signal), with the resulting signal being multiplied by a predetermined scale factor.
Several arrangements of the above-discussed type wherein accelerometers are mounted for vibration or oscillation (rather than rotation) so as to supply a signal that can be processed to provide the specific force along one axis of the coordinate system and the angular rotation associated with another axis of a coordinate system are disclosed in Shmuel J. Merhav, U.S. patent application Ser. No. 528,776, filed Sept. 2, 1983. That patent application is entitled "Apparatus For Measuring Inertial Specific Force and Angular Rate of A Moving Body, And Accelerometer Assemblies Particularly Useful Therein," and is assigned to the assignee of the present invention.
In the first arrangement of the referenced patent application, each accelerometer is mounted so that its force sensing axis extends orthogonally from a plane that includes two axes of a Cartesian coordinate system (e.g., the Y-Z plane) and so that the accelerometer force sensitive axis intersects one of the two axes (e.g., the Z axis) at a point which may be remote from the origin of the coordinate system. In addition, each accelerometer is mounted or internally configured so that accelerometer force sensitive axis is displaced back and forth along a coordinate axis in the reference plane at a uniform cyclic rate. As is illustrated in the referenced patent application, the signal provided by such an accelerometer can be processed in the manner disclosed in the above-referenced U.S. Pat. No. 4,445,376 to supply the specific force component relative to the coordinate axis that is parallel to the force sensing axis of the accelerometer and to supply the angular rate component for a second coordinate axis, which is mutually orthogonal to the axis along which the accelerometer is displaced and the coordinate axis that is in alignment with the accelerometer force sensitive axis. For example, an accelerometer mounted with its force sensitive axis orthogonal to the Y-Z plane and configured for cyclic displacement of the force sensitive axis in the Z direction (along the Z axis), provides an output signal that can be processed to obtain the X axis component of specific force and the Y axis component of angular rate. Thus, by utilizing three accelerometers that are mounted for linear displacement (cyclic motion) along each of the three axes of a coordinate system, a complete specification of the movement of a body can be obtained.
The above-referenced patent application also discloses three arrangements wherein a pair of accelerometers is associated with a coordinate axis of a moving body to generate a signal that can be processed to obtain the specific force component relative to one coordinate axis of the body and the angular rate component for a different coordinate axis of the body. In one of these paired accelerometer arrangements, the force sensitive axes of the two accelerometers are parallel to one another and parallel to the coordinate axis for which a specific force measurement is to be obtained. In addition, the accelerometers are positioned such that the force sensitive axis of each accelerometer is equally spaced apart from a second coordinate axis and is perpendicular to a line that extends through the second coordinate axis. In this arrangement, the accelerometers are driven or internally configured so that the force sensitive axes of the accelerometers cyclically rotate through a small angle of deflection. This causes the force sensitive axes of the two accelerometers to cyclically move back and forth along lines that are equally spaced apart from the second coordinate axis. For example, in such an arrangement, the force sensing axes of a pair of accelerometers that are mounted for providing a signal that can be processed to obtain the X axis component of specific force and the Y axis component of angular rate are: (a) equally spaced apart from the Z coordinate axis; (b) mounted with the force sensitive axes extending in the X direction; and, (c) configured and arranged so that the accelerometer force sensing axes move cyclically back and forth along arcuate paths (chords of a circle) that approximate straight lines that are parallel to the Z axis and lie in the Y-Z plane.
In a second paired accelerometer arrangement of the referenced patent application, each accelerometer of an accelerometer pair is equally spaced apart from a coordinate axis with the force sensitive axes of the two accelerometers being colinear with a line that extends through a point on the same coordinate axis. In this arrangement, the accelerometers are aligned with a second axis of the coordinate system and are mounted for sensing oppositely directed specific forces. Further, the accelerometers are cyclically and simultaneously moved back and forth along a small arcuate path that lies in a plane that includes the force sensitive axes of the accelerometers and the coordinate axis with which the force sensitive axes of the accelerometers intersect. For example, in such an arrangement, a pair of accelerometers that are mounted with the force sensitive axes pointing in the X direction oscillate at a uniform cyclic rate along oppositely disposed chords of a circle that lies in the X-Z coordinate plane. As is the case with the other arrangements disclosed in the previously mentioned patent and the referenced patent application, the signal supplied by the accelerometers whose force sensitive axes extend in the X direction can be processed to provide a signal representative of the X axis specific force component and a signal representative of the Y axis angular rate component.
In the third paired accelerometer arrangement disclosed in the referenced patent application, the spatial relationship between the force sensing axes of each accelerometer pair and the coordinate system is identical to the above-discussed second arrangement. The difference between the second and third arrangements is that the accelerometers of the third arrangement are configured and arranged for cyclical displacement of the force sensitive axes of the two accelerometers of each accelerometer pair along straight line paths (with both force sensitive axes moving in the same coordinate direction) rather than being configured and arranged for cyclically displacing the force sensitive axes along chords of a circle that approximate straight lines (with the two force sensitive axes moving in opposite directions). In this third arrangement, the signals provided by each pair of accelerometers can be processed to supply a signal representative of the specific force component for the coordinate axis that is parallel to the force sensitive axes of the accelerometers and to supply the angular rate component for the coordinate axes that is normal to the plane in which the force sensitive axes of the accelerometers oscillate.
As is disclosed in the referenced patent application, when the signals provided by each pair of accelerometers in the three disclosed paired accelerometer arrangements are added and subtracted, two separate signals are obtained (a "sum" signal and a "difference" signal), with one of the signals being substantially devoid of the specific force component and the other signal being substantially devoid of the angular rate component. In addition, the signal-to-noise ratio of the sum and difference signal theoretically is improved by a factor of .sqroot.2 relative to the signals provided by each of the accelerometers. The sum and difference signals obtained from each accelerometer pair are then separately processed in the manner disclosed in the referenced U.S. patent to provide a signal representative of the desired specific force component and a signal representative of the desired angular rate component.
Although the synchronous detection signal process that is disclosed in the referenced patent and referenced patent application can be satisfactory in some situations, certain disadvantages and drawbacks are encountered. Firstly, the specific force signal and rate signal that are provided may include a signal component (ripple) at the signal processing modulation frequency (i.e., at the frequency at which the accelerometers are rotated or oscillated). Removal of this ripple component with a low-pass filter can decrease the bandwidth of the accelerometer system to an unacceptable degree. At the very least, the bandwidth of the signal processing arrangement disclosed in the referenced patent and patent application is limited to one-half the modulation frequency and, angular rates averaged over each period may be somewhat in error due to uncompensated weighting effects associated with the oscillation waveform. Further, the signal processing disclosed in the referenced patent application and patent is typically implemented with analog circuit devices. Current commercially available devices of the type used in such circuitry often exhibit temperature dependency or other characteristics that can cause errors in the specific force and angular rate signals (drift).